Helical spring



June 25, 1946.

A. RAsPET HELICAL SPRING `Filed March 27, 1942 a b c de fg .5 (jm/venivo@ Aaga QCM/@QT Spr/ny Lny/i Patented June 25,` 1946 UNITED STATES PATENT OFFICE 2,402,666 HELICALsPsING August Rusnet, Hyattsville, ma. `Animation Maren 21, 1942, smal No. 436,390

u 1 claim. iol. zei-1) (Granted under the act of March 3, 1883, as

The invention described hereinI if` patented,

l may be manufactured and used by or for the Government for governmental purposes without the payment to me of any royalty thereon.

My invention relates to helical springs of the type which wind or unwind `upon elongation. These springs have been constructed empirically with the 'result that their rotational response to elongation `was not a determinable function of that elongation. Therefore, such springs were not suitable for use in measuring instruments, and theiruse was especially objectionable in instruments produced in quantity. A

An object of this invention is to provide a helical spring the behavior of which can be predicted with mathematical exactness.

'I'he features of the invention are illustrated in the accompanying drawing, wherein: Fig. l is a view in elevation oi a helical spring formed o! an elastic strip having its width parallel tothe axis of the helix;

amended April 30, 1928; 370 0. G. 757) Fig. 2 is a `view similar to Fig. 1, but showing i a spring formed of an elastic strip with its width parallel to the radii of the helix;

Figs.` 3, 4 and 5 are graphs illustrating the logarithmic, parabolic and vlinear responses respectively of helical springs made according to thisinvention; and i Fig. 6` is a detail view illustrating a representative ygroup ot crosssections of elastic strips which may be used in constructing helical springs.

Helical springs constructed ot an elasticstrip will wind or unwind when elongated according to the relative rigidity of the cross section of the strip to bending as compared to the sections torsional rigidity.` The tendency of such a .spring to wind or unwind depends upon the relative torsional and bending rigidities o! the strip. as well as-upon the pitch angle and the radius of the helix. Specically this invention proposes to utilise the variation in pitch angle to obtain certain mathematical relationshipsbetween the elongation and the amount` of turning of the helical `spring.

In the illustration Fig. une strip is a nat ribbon wound with its greater cross-sectional dimensionparallel to the axis of the helix. In this configuration of the helical spring the "spring tendstounwindwhenelongated. Thebasicreaterms of the various parameters.

son for this behavior lies in the tact that the potentialenergy of such a spring is storedf in the bending and intwlsting of the cross section of the strip. In the spring illustrated in Fig. 1 the energy stored in bending the cross section about a radius of the section at that point is greater than that stored in twisting the section. This results in a rotation of the free end o! the spring in such a direction that the spring unwlnds.

On the other hand. if the spring is Wound as shown in Fig. 2, the spring is more rigid to torsion than to bending in its section and there consequently results a tendency for the spring to wind up.

A more rigorous description of the behavior of a helical spring is that furnished by mathematical analysis. The earlles mathematical analysis of the behavior of helical springs dates to Mossotti 1817. Later, Kirchoii, Thomson and Tait, and Clebsch added their endeavors to the solution of the problem. Formally the treatment of this problem consists in setting up the relation expressing the potential energy of the spring in The potential energy is differentiated i'or the incremental rotation and elongation. The resulting relations for a ilat strip oi radial thickness a and longitudinal width b are:

where w is the axial force tending to elongate the spring,

' (A) This invention is based on the principle discovered by applicant that from the quotient of the above relations the rotatory magnincanon expressed as turns of the spring per unit elongation can be obtained. The magnification is found 'I'he rotatory magnification is shown by this newly discovered relation to be clearly dependent on the radius R. of the spring: the smaller the radius the greater the magnification. Further. it can be seen from this relation that the magninoatlon will be greatestwhen the value ot asb departs substantially from unity. In the case where is small (much less than unity) the spring will be as in Fig. 1. In the second case, azb much' greater than unity, the spring will have the conilguration of Fig. 2.

(B) When the ratio a:b is small (Fig. l) the rotary magnincation becomes:

and having selected a material with a certain 9 as shown by newly discovered relation [3l above. the magnification is then dependent only on the value of a. `It is the essence of this invention w control the variation in magnincation by selectters. that a logarithmic relationship of rotation and elongation is desired. Such a condition obtains if:

where' b=the total turns of spring, and k is a constant.

From newly discovered relations [5l and [4], it 'follows that for this condition:r`

A solution of the latter equation for a furnishes the value of the pitch angle of the helical spring for which the rotatory magnification is inversely yproportional to the length of the spring; wherefore the rotation of the spring is proportional to the logarithm of the length of the spring. This functional relation, when the rotation is plotted 4. against the logarithm of the springs length, graphs as a straight line, Fig. 3.

(B-2) In another application of the helical spring described herein one may desire a Darabolic relation between the rotation and the length ofthe spring. viz:

=cL*, where c is a constant l'll Such a behavior is attained as above shown when When this equation is solved fora, the helical spring constructed with that value of a will possess a parabolic relation between rotation and the length of the spring. For such a behavior a graph of the rotation of the spring against the square of the length of the spring will b e a straight line. Such a graph is shown in Fig. 4. A spring of this design used in an airspeed indicator results in a uniform scale of speed instead of the usual non-uniform scale.

(B3) 'I'he most common use of helical springs which wind or unwind is that in which a uniform rotatory response to elongation is desired (Fig. 5). For this. the linear case;j the rotatory magnification must be constant with changes in length oi' the spring:

gif-h, when h i a mutant [lo] n t web Solving the last equation for a will furnish the pitch angle around which the helical spring will behave linearly. In the eld of instrumentation this type ci spring has wide application to pressure gages, vacuum gages. barometers and electrical measuring instruments.

(C) For illustrating the method described in this invention the mathematical formulae have been developed forthe case of a helical spring wound of a ilat ribbon of an elastic material. It must be emphasized that the method is perfectly general in that one may simply substitute for the torsional and bending energy relations on the flat strip the relations applying to cross sections of other coniigurations. It happens that the greatest magnification is obtained by the use oi' a hat strip. ybut for certain applications other cross sectional forms may be desired. Various cross sections of springs which will respond to this treatment are illustrated in Fig. 6, cross sections a to a, inclusive.

From the foregoing description of preferred embodiments of myinvention it will be readily apparent to those skilled in the art that the invention is not limited to the particular embodiments disclosed to illustrate the same.

I claim as my invention and desire tosecure by Letters Patent:

A helical spring having a pitch angle for which the rotary magnication expressed as turns ctthespringpertmitelongationisinvenelypro- 5 i 6 portlonll to the length of the spring. that ls. in R is the radius o! the spring. I the total number which d of turns o fthe spring. and K is a constant of d0 K sensitivity. the equation being: 3L 'I while l i i 5 i d i ,s um mum Wouldn expressed as mms which. when solved i'or tan a, yields:

of the spring per unit elongation. L is the length 10 o! the helix and K is s constant, where the pitch t unie (s) is given by solving the equation nereinn nfter following for the value of (a) after introdueinz the selected values ot radial thickness (a). um longitudinal width u. they Yoann is AUGUST RASPET- modulus (q) and the shear modulus (n). where y 

